Finite Group Databasebeta

← #11910044

Subgroups — #11910044

Order 1152.

2215 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2C3×#5532C211yesmaximal, characteristic, complemented
3C3×#5529C211yesmaximal, characteristic, complemented
4#10595033C211yesmaximal, characteristic, complemented
5#10594965C211yesmaximal, characteristic, complemented
6#10594919C211yesmaximal, characteristic, complemented
7#10594916C211yesmaximal, characteristic, complemented
8#10594566C211yesmaximal, characteristic, complemented
9#10594559C211yesmaximal, characteristic, complemented
10#10594525C211yesmaximal, characteristic, complemented
11#10594501C211yesmaximal, characteristic, complemented
12#10594359C211yesmaximal, characteristic, complemented
13#10594357C211yesmaximal, characteristic, complemented
14#10594343C211yesmaximal, characteristic, complemented
15#10594318C211yesmaximal, characteristic, complemented
16#10594219C212yesmaximal, complemented
17#10594152C212yesmaximal, complemented
18#10594151C212yesmaximal, complemented
19#10594124C212yesmaximal, complemented
20#10593980C212yesmaximal, complemented
21#10593943C212yesmaximal, complemented
22#10593930C212yesmaximal, complemented
23#10593918C212yesmaximal, complemented
24#86965—31nomaximal
25#86843—31nomaximal
26C2×#3828C2211yescharacteristic
27C2×#3795C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×#117C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31#64102C2211yescharacteristic
32#64102C2211yescharacteristic
33#64096C2211yescharacteristic
34#64096C2211yescharacteristic
35#64090C2212yes—
36#64090C2212yes—
37#64081C2212yes—
38C42×C3⋊D3C2212yes—
39C3×#930C2211yescharacteristic
40C3×C4×#67C2211yescharacteristic
41C3×C4×#67C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C3×#897C2211yescharacteristic
44C3×#895C2211yescharacteristic
45C3×#893C2211yescharacteristic
46C3×#892C2211yescharacteristic
47C3×D3×C4⋊C4C2211yescharacteristic
48C3×#890C2211yescharacteristic
49C3×#888C2211yescharacteristic
50C3×#887C2211yescharacteristic
51C3×#885C2212yes—
52C3×#884C2212yes—
53C3×#883C2212yes—
54C3×#879C2212yes—
55C3×#875C2212yes—
56C3×#872C2212yes—
57C3×#872C2212yes—
58C3×#870C2212yes—
59#63982C2211yescharacteristic
60#63980C2211yescharacteristic
61#63979C2212yes—
62#67⋊Dic3C2212yes—
63#63971C2212yes—
64#63971C2212yes—
65#63962C2211yescharacteristic
66#63962C2212yes—
67#63962C2211yescharacteristic
68#63953C2212yes—
69C4×#627C2211yescharacteristic
70C4×#627C2212yes—
71#63916C2212yes—
72#63915C2211yescharacteristic
73#63915C2212yes—
74#63912C2212yes—
75#63911C2211yescharacteristic
76#63909C2211yescharacteristic
77#63909C2211yescharacteristic
78#63907C2212yes—
79#63906C2212yes—
80C4×#626C2212yes—
81C4×#626C2212yes—
82C4×#625C2212yes—
83C4×#625C2211yescharacteristic
84#63899C2212yes—
85#63898C2211yescharacteristic
86#63898C2212yes—
87#63890C2212yes—
88#63886C2212yes—
89#63885C2212yes—
90#63881C2212yes—
91#63881C2212yes—
92#63879C2212yes—
93#63878C2212yes—
94#63878C2212yes—
95#63878C2212yes—
96#63877C2212yes—
97D3×Dic3⋊C4C2212yes—
98#63872C2211yescharacteristic
99#63871C2212yes—
100#63870C2212yes—
101#63870C2211yescharacteristic
102#63868C2212yes—
103#63865C2212yes—
104#63864C2211yescharacteristic
105#63863C2211yescharacteristic
106#63862C2212yes—
107#63862C2211yescharacteristic
108#63862C2211yescharacteristic
109#63855C2211yescharacteristic
110#63855C2211yescharacteristic
111#63853C2212yes—
112#63853C2212yes—
113#63853C2212yes—
114#63853C2212yes—
115#63852C2212yes—
116#63850C2212yes—
117#63848C2212yes—
118#63847C2212yes—
119#63844C2211yescharacteristic
120#63844C2211yescharacteristic
121#63843C2212yes—
122#63843C2211yescharacteristic
123#63839C2212yes—
124#63837C2212yes—
125C3×#555—31no—
126C3×#552—31no—
127#5733—31no—
128#5721—31no—
129#5710—32no—
130#5709—32no—
131#5697—31no—
132#5693—32no—
133#5691—32no—
134#5685—31no—
135#5681—32no—
136#5680—32no—
137#5670—32no—
138#5669—32no—
139#5664—32no—
140#5663—32no—
141#5643—31no—
142#5633—31no—
143#5633—31no—
144#5624—31no—
145#5619—31no—
146#5615—32no—
147#5601—32no—
148#5600—31no—
149#5599—31no—
150#5598—31no—
151#5585—31no—
152#5572—31no—
153#5559—31no—
154#5553—31no—
155#5552—31no—
156#5546—31no—
157#5538—31no—
158#5538—31no—
159#5532—32no—
160#5532D311yescharacteristic, complemented
161#5531—32no—
162#5530—31no—
163#5529D311yescharacteristic, complemented
164#5528—32no—
165#5528—32no—
166#5522—31no—
167#5522—31no—
168#5522—61no—
169#5516—31no—
170#5514—31no—
171#5504—31no—
172C22×C32×C4C2311yescharacteristic
173C2×#638C2312yes—
174C22×C3⋊Dic3C2311yescharacteristic
175C22×C3⋊Dic3C2311yescharacteristic
176#3828—24no—
177C2×C4⋊(C3⋊D3)C2311yescharacteristic
178C2×C4×C3⋊D3C2312yes—
179C2×C4×C3⋊D3C2312yes—
180C2×C4×C3⋊D3C2312yes—
181C2×#634C2311yescharacteristic
182C2×C3×#67C2311yescharacteristic
183C2×C3×#67C2311yescharacteristic
184C2×C3×#67C2312yes—
185C2×C3×D12C2311yescharacteristic
186C2×C3×D12C2312yes—
187C2×C3×C4×D3C2311yescharacteristic
188C2×C3×C4×D3C2311yescharacteristic
189C2×C3×C4×D3C2312yes—
190C2×C3×C4×D3C2312yes—
191C2×C3×Dic6C2311yescharacteristic
192C2×C3×Dic6C2312yes—
193C2×#627C2312yes—
194C2×#627C2311yescharacteristic
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#626C2312yes—
198C2×#626C2312yes—
199C2×#625C2312yes—
200C2×#625C2311yescharacteristic
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2312yes—
204#3795—24no—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C4⋊C4C2311yescharacteristic
208C32×C22⋊C4C2312yes—
209C32×C42C2312yes—
210#3752C2312yes—
211#3752C2312yes—
212#3750C2312yes—
213#3750C2312yes—
214C4×C3⋊Dic3C2311yescharacteristic
215C4×C3⋊Dic3C2312yes—
216C4×C3⋊Dic3C2312yes—
217C4×C3⋊Dic3C2311yescharacteristic
218C4×C3⋊Dic3C2311yescharacteristic
219C4×C3⋊Dic3C2311yescharacteristic
220C3×#217C2311yescharacteristic
221C3×#217C2312yes—
222C3×#217C2311yescharacteristic
223C3×(C2×D3)⋊C4C2312yes—
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2311yescharacteristic
228C3×(C2×D3)⋊C4C2311yescharacteristic
229C3×(C2×D3)⋊C4C2312yes—
230C3×C4⋊Dic3C2312yes—
231C3×C4⋊Dic3C2312yes—
232C3×C4⋊Dic3C2311yescharacteristic
233C3×C4⋊Dic3C2311yescharacteristic
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×Dic3⋊C4C2312yes—
237C3×Dic3⋊C4C2312yes—
238C3×Dic3⋊C4C2312yes—
239C3×Dic3⋊C4C2311yescharacteristic
240C3×Dic3⋊C4C2311yescharacteristic
241C3×C4×Dic3C2312yes—
242C3×C4×Dic3C2312yes—
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245#3724C2312yes—
246#3724C2312yes—
247#3724C2311yescharacteristic
248#3724C2311yescharacteristic
249Dic3⋊Dic3C2311yescharacteristic
250Dic3⋊Dic3C2312yes—
251Dic3⋊Dic3C2311yescharacteristic
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2311yescharacteristic
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2311yescharacteristic
258#3722C2312yes—
259#3722C2312yes—
260#3722C2312yes—
261#3722C2312yes—
262(C2×D3)⋊Dic3C2312yes—
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2311yescharacteristic
265(C2×D3)⋊Dic3C2312yes—
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2311yescharacteristic
268(C2×D3)⋊Dic3C2311yescharacteristic
269(C2×D3)⋊Dic3C2311yescharacteristic
270(C2×D3)⋊Dic3C2311yescharacteristic
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3524—91noSylow
275C2×D3×Q8—31no—
276C2×#237—31no—
277C2×#235—31no—
278C2×#235—31no—
279C2×#235—31no—
280C2×#235—61no—
281C22×Dic6—31no—
282C3×C4⋊Q8—31no—
283C3×#126—32no—
284C3×#125—31no—
285C3×#125—32no—
286C3×#124—32no—
287C3×#124—32no—
288C3×#123—32no—
289C3×C22⋊Q8—31no—
290C3×C22⋊Q8—31no—
291C3×#121—31no—
292C3×#121—31no—
293C3×#121—32no—
294C3×C4×Q8—31no—
295C3×C4×D4—31no—
296C3×C4×D4—31no—
297C3×C4×D4—31no—
298C3×#117—21no—
299C3×#117—31no—
300C3×#117—32no—
301C3×#117—32no—
302C3×#117C2×D311yescharacteristic
303C3×#117C2×D311yescharacteristic
304C2×C3×C4⋊C4—31no—
305#947—31no—
306#947—32no—
307#947—31no—
308#946—32no—
309Q8×Dic3—31no—
310Q8×Dic3—32no—
311#944—32no—
312#940—32no—
313#940—32no—
314#940—31no—
315#939—31no—
316#939—31no—
317#939—32no—
318#939—32no—
319#939—32no—
320#939—32no—
321#938—32no—
322#936—31no—
323#935—31no—
324#935—32no—
325#935—31no—
326D4×Dic3—32no—
327D4×Dic3—32no—
328D4×Dic3—31no—
329#930—32no—
330#930—31no—
331#930—31no—
332#930C2×D311yescharacteristic
333#929—32no—
334C4×#67—31no—
335C4×#67—32no—
336C4×#67—32no—
337C4×#67—31no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341C4×#67C2×D311yescharacteristic
342C4×#67C2×D311yescharacteristic
343#926—31no—
344#926—31no—
345#924C2×D311yescharacteristic
346C2×Dic3⋊C4—32no—
347C2×C4×Dic3—31no—
348C2×C4×Dic3—31no—
349C2×C4×Dic3—61no—
350#898—31no—
351#898—32no—
352#898—31no—
353#898—32no—
354#898—32no—
355#898—32no—
356#897—32no—
357#897C2×D311yescharacteristic
358#896—32no—
359#896—32no—
360#896—32no—
361#895—32no—
362#895—32no—
363#895—31no—
364#895—31no—
365#895C2×D311yescharacteristic
366#894—32no—
367#894—32no—
368#894—32no—
369#894—32no—
370#894—32no—
371#894—32no—
372#893—32no—
373#893—31no—
374#893—31no—
375#893—31no—
376#893—31no—
377#893—31no—
378#893—32no—
379#893—32no—
380#893—61no—
381#893—61no—
382#893C2×D311yescharacteristic
383#892—32no—
384#892—32no—
385#892—32no—
386#892C2×D311yescharacteristic
387D3×C4⋊C4—32no—
388D3×C4⋊C4C2×D311yescharacteristic
389#890—31no—
390#890—31no—
391#890C2×D311yescharacteristic
392#889—32no—
393#889—32no—
394#889—32no—
395#889—31no—
396#889—32no—
397#889—31no—
398#888—32no—
399#888C2×D311yescharacteristic
400#887—32no—
401#887—31no—
402#887—31no—
403#887—31no—
404#887—31no—
405#887—31no—
406#887—31no—
407#887—32no—
408#887—31no—
409#887—61no—
410#887—61no—
411#887C2×D311yescharacteristic
412#886—32no—
413#886—31no—
414#886—31no—
415#886—32no—
416#885—32no—
417#885—32no—
418#885—32no—
419#885—32no—
420#885—31no—
421#885—32no—
422#885—31no—
423#885—32no—
424#885C2×D312yes—
425#884—32no—
426#884—32no—
427#884—32no—
428#884—32no—
429#884—32no—
430#884—32no—
431#884C2×D312yes—
432#883—32no—
433#883—32no—
434#883—32no—
435#883—32no—
436#883C2×D312yes—
437#67⋊C4—32no—
438#67⋊C4—32no—
439#67⋊C4—32no—
440#67⋊C4—32no—
441#67⋊C4—32no—
442#67⋊C4—32no—
443#67⋊C4—32no—
444#67⋊C4—32no—
445#67⋊C4—62no—
446#67⋊C4—62no—
447#879—31no—
448#879—32no—
449#879—31no—
450#879C2×D312yes—
451#878—31no—
452#878—31no—
453#878—32no—
454#877—32no—
455#877—32no—
456#877—32no—
457#877—32no—
458#876—32no—
459#875—31no—
460#875—32no—
461#875C2×D312yes—
462#874—31no—
463C4×D12—32no—
464C4×D12—32no—
465#872—31no—
466#872—31no—
467#872—32no—
468#872—32no—
469#872—32no—
470#872—62no—
471#872C2×D312yes—
472#872C2×D312yes—
473C42×D3—32no—
474C42×D3—32no—
475C42×D3—62no—
476#870C2×D312yes—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—32no—
481C4×Dic6—31no—
482C4×Dic6—32no—
483C4×Dic6—31no—
484C23×C32C2411yescharacteristic
485C22×C3⋊D3C2412yes—
486C22×C3×D3C2411yescharacteristic
487C22×C3×D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C2×C32×C4—22no—
490C2×C32×C4C2412yes—
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2412yes—
493C2×C32×C4C2411yescharacteristic
494#638—24no—
495C2×C3⋊Dic3—41no—
496C2×C3⋊Dic3—41no—
497C2×C3⋊Dic3C2411yescharacteristic
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C2×C3⋊Dic3C2411yescharacteristic
501C2×C3⋊Dic3C2412yes—
502C4⋊(C3⋊D3)—22no—
503C4×C3⋊D3—24no—
504C4×C3⋊D3—42no—
505C4×C3⋊D3—42no—
506#634#4114yes—
507C3×#67—41no—
508C3×#67—42no—
509C3×#67—41no—
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2412yes—
513C2×C3×Dic3C2412yes—
514C2×C3×Dic3C2412yes—
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2411yescharacteristic
519C3×D12—22no—
520C3×D12—42no—
521C3×C4×D3—22no—
522C3×C4×D3—22no—
523C3×C4×D3—42no—
524C3×C4×D3—42no—
525C3×Dic6—22no—
526C3×Dic6—42no—
527#627—24no—
528#627—41no—
529#626—42no—
530#626—42no—
531#626—42no—
532#626—42no—
533#625—24no—
534#625—41no—
535D3×Dic3—24no—
536D3×Dic3—24no—
537D3×Dic3—42no—
538#559—91no—
539#559—92no—
540#557—91no—
541#555—31no—
542#555—92no—
543#553—91no—
544#553—92no—
545#552—31no—
546#552—92no—
547#550—91no—
548#548—91no—
549#548—91no—
550#542—91no—
551#542—92no—
552#540—92no—
553#540—91no—
554#529—92no—
555#529—91no—
556#529—91no—
557#529—92no—
558#520—91no—
559#519—91no—
560C4×#41—91no—
561C2×C3×Q8—31no—
562C2×C3×Q8—32no—
563C2×C3×D4—32no—
564C2×C3×D4—31no—
565C2×C3×D4—31no—
566C2×C3×D4—31no—
567C2×C3×D4—32no—
568C22×C3×C4—21no—
569C22×C3×C4—31no—
570C22×C3×C4—31no—
571C22×C3×C4—32no—
572C22×C3×C4—32no—
573C22×C3×C4C22×D311yescharacteristic
574C22×C3×C4C22×D311yescharacteristic
575C2×#67—32no—
576C2×#67—32no—
577C2×#67—32no—
578C2×#67—32no—
579C2×#67—31no—
580C2×#67—31no—
581C2×#67—32no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—62no—
586C2×#67C22×D312yes—
587C2×#67C22×D311yescharacteristic
588C2×#67C22×D311yescharacteristic
589C22×Dic3—31no—
590C22×Dic3—31no—
591C22×Dic3—31no—
592C22×Dic3—31no—
593C22×Dic3—32no—
594C22×Dic3—32no—
595C22×Dic3—32no—
596C22×Dic3—61no—
597C22×Dic3—61no—
598D3×Q8—64no—
599#237—64no—
600#235—64no—
601#235—64no—
602#235—64no—
603#235—68no—
604C2×D12—31no—
605C2×D12—31no—
606C2×D12—32no—
607C2×D12—32no—
608C2×D12—32no—
609C2×D12—32no—
610C2×D12—61no—
611C2×D12C22×D311yescharacteristic
612C2×D12C22×D312yes—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—62no—
623C2×C4×D3—62no—
624C2×C4×D3—62no—
625C2×C4×D3C22×D311yescharacteristic
626C2×C4×D3C22×D311yescharacteristic
627C2×C4×D3C22×D312yes—
628C2×C4×D3C22×D312yes—
629C2×Dic6—31no—
630C2×Dic6—31no—
631C2×Dic6—32no—
632C2×Dic6—32no—
633C2×Dic6—31no—
634C2×Dic6—31no—
635C2×Dic6—61no—
636C2×Dic6—64no—
637C2×Dic6C22×D311yescharacteristic
638C2×Dic6C22×D312yes—
639C3×C4⋊C4—21no—
640C3×C4⋊C4—21no—
641C3×C4⋊C4—31no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—31no—
644C3×C4⋊C4—32no—
645C3×C4⋊C4—32no—
646C3×C4⋊C4—32no—
647C3×C4⋊C4—31no—
648C3×C4⋊C4—31no—
649C3×C4⋊C4—32no—
650C3×C4⋊C4—32no—
651C3×C4⋊C4—32no—
652C3×C4⋊C4C22×D311yescharacteristic
653C3×C4⋊C4C22×D311yescharacteristic
654C3×C4⋊C4C22×D311yescharacteristic
655C3×C4⋊C4C22×D311yescharacteristic
656C3×C22⋊C4—22no—
657C3×C22⋊C4—31no—
658C3×C22⋊C4—31no—
659C3×C22⋊C4—32no—
660C3×C22⋊C4—32no—
661C3×C22⋊C4—32no—
662C3×C22⋊C4—32no—
663C3×C22⋊C4—32no—
664C3×C22⋊C4—31no—
665C3×C22⋊C4—31no—
666C3×C22⋊C4—32no—
667C3×C22⋊C4C22×D312yes—
668C3×C22⋊C4C22×D312yes—
669C3×C42—22no—
670C3×C42—31no—
671C3×C42—31no—
672C3×C42—32no—
673C3×C42—32no—
674C3×C42C22×D312yes—
675C3×C42C22×D312yes—
676#217—31no—
677#217—31no—
678#217—32no—
679#217—32no—
680#217—31no—
681#217—31no—
682#217—32no—
683#217—31no—
684#217—31no—
685#217C22×D311yescharacteristic
686#217C22×D311yescharacteristic
687#217C22×D312yes—
688(C2×D3)⋊C4—31no—
689(C2×D3)⋊C4—31no—
690(C2×D3)⋊C4—31no—
691(C2×D3)⋊C4—31no—
692(C2×D3)⋊C4—31no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—32no—
695(C2×D3)⋊C4—32no—
696(C2×D3)⋊C4—31no—
697(C2×D3)⋊C4—32no—
698(C2×D3)⋊C4—32no—
699(C2×D3)⋊C4—32no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—32no—
702(C2×D3)⋊C4—32no—
703(C2×D3)⋊C4—32no—
704(C2×D3)⋊C4—32no—
705(C2×D3)⋊C4—32no—
706(C2×D3)⋊C4—32no—
707(C2×D3)⋊C4—32no—
708(C2×D3)⋊C4—32no—
709(C2×D3)⋊C4—62no—
710(C2×D3)⋊C4—62no—
711(C2×D3)⋊C4C22×D312yes—
712(C2×D3)⋊C4C22×D311yescharacteristic
713(C2×D3)⋊C4C22×D312yes—
714(C2×D3)⋊C4C22×D312yes—
715(C2×D3)⋊C4C22×D312yes—
716(C2×D3)⋊C4C22×D312yes—
717(C2×D3)⋊C4C22×D311yescharacteristic
718C4⋊Dic3—31no—
719C4⋊Dic3—31no—
720C4⋊Dic3—31no—
721C4⋊Dic3—31no—
722C4⋊Dic3—32no—
723C4⋊Dic3—32no—
724C4⋊Dic3—31no—
725C4⋊Dic3—32no—
726C4⋊Dic3—31no—
727C4⋊Dic3C22×D311yescharacteristic
728C4⋊Dic3C22×D311yescharacteristic
729C4⋊Dic3C22×D312yes—
730C4⋊Dic3C22×D312yes—
731Dic3⋊C4—32no—
732Dic3⋊C4—32no—
733Dic3⋊C4—32no—
734Dic3⋊C4—32no—
735Dic3⋊C4—31no—
736Dic3⋊C4—32no—
737Dic3⋊C4—32no—
738Dic3⋊C4—32no—
739Dic3⋊C4—31no—
740Dic3⋊C4—31no—
741Dic3⋊C4—31no—
742Dic3⋊C4—32no—
743Dic3⋊C4—31no—
744Dic3⋊C4—31no—
745Dic3⋊C4—31no—
746Dic3⋊C4—31no—
747Dic3⋊C4—31no—
748Dic3⋊C4—32no—
749Dic3⋊C4—31no—
750Dic3⋊C4—32no—
751Dic3⋊C4—32no—
752Dic3⋊C4—62no—
753Dic3⋊C4—62no—
754Dic3⋊C4C22×D312yes—
755Dic3⋊C4C22×D311yescharacteristic
756Dic3⋊C4C22×D312yes—
757Dic3⋊C4C22×D312yes—
758Dic3⋊C4C22×D311yescharacteristic
759Dic3⋊C4C22×D312yes—
760Dic3⋊C4C22×D312yes—
761C4×Dic3—32no—
762C4×Dic3—32no—
763C4×Dic3—31no—
764C4×Dic3—31no—
765C4×Dic3—31no—
766C4×Dic3—31no—
767C4×Dic3—32no—
768C4×Dic3—32no—
769C4×Dic3—31no—
770C4×Dic3—31no—
771C4×Dic3—31no—
772C4×Dic3—31no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—32no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—32no—
779C4×Dic3—61no—
780C4×Dic3—62no—
781C4×Dic3—62no—
782C4×Dic3—61no—
783C4×Dic3—61no—
784C4×Dic3—61no—
785C4×Dic3C22×D312yes—
786C4×Dic3C22×D312yes—
787C4×Dic3C22×D311yescharacteristic
788C4×Dic3C22×D311yescharacteristic
789C22×C32—21no—
790C22×C32—21no—
791C22×C32—21no—
792C22×C32C2511yescharacteristic
793C2×C3⋊D3—22no—
794C2×C3⋊D3—22no—
795C2×C3⋊D3—22no—
796C2×C3×D3—21no—
797C2×C3×D3—22no—
798C2×C3×D3—21no—
799C2×C3×D3—22no—
800C2×C3×D3—21no—
801C2×C3×D3—21no—
802C2×C3×D3—21no—
803C2×C3×D3—22no—
804C2×C3×D3—21no—
805C32×C4—21no—
806C32×C4—22no—
807C32×C4—22no—
808C32×C4C2×#4112yes—
809C3⋊Dic3—21no—
810C3⋊Dic3—21no—
811C3⋊Dic3—21no—
812C3⋊Dic3—21no—
813C3⋊Dic3C2×#4114yes—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—22no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—22no—
821C3×Dic3—21no—
822C3×Dic3—21no—
823C2×#41—91no—
824C2×#41—91no—
825C22×Q8—91no—
826C4⋊Q8—31no—
827C4⋊Q8—92no—
828#127—91no—
829#127—92no—
830#126—32no—
831#126—92no—
832#126—91no—
833#126—92no—
834#126—91no—
835#126—92no—
836#125—31no—
837#125—32no—
838#125—91no—
839#125—92no—
840#125—91no—
841#125—92no—
842#124—32no—
843#124—32no—
844#124—92no—
845#124—91no—
846#124—92no—
847#124—91no—
848#124—92no—
849#124—92no—
850#124—91no—
851#123—32no—
852#123—92no—
853#123—92no—
854#123—92no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—91no—
859#123—91no—
860#123—92no—
861C22⋊Q8—31no—
862C22⋊Q8—31no—
863C22⋊Q8—91no—
864C22⋊Q8—92no—
865C22⋊Q8—92no—
866C22⋊Q8—92no—
867#121—31no—
868#121—31no—
869#121—32no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—92no—
874#121—92no—
875#121—91no—
876#121—91no—
877#121—92no—
878#121—92no—
879#121—91no—
880C4×Q8—31no—
881C4×Q8—92no—
882C4×Q8—91no—
883C4×Q8—91no—
884C4×Q8—92no—
885C4×Q8—91no—
886C4×Q8—91no—
887C4×Q8—92no—
888C4×Q8—91no—
889C4×Q8—91no—
890C4×D4—31no—
891C4×D4—31no—
892C4×D4—31no—
893C4×D4—92no—
894C4×D4—92no—
895C4×D4—92no—
896C4×D4—92no—
897C4×D4—92no—
898C4×D4—92no—
899C4×D4—91no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—91no—
903C4×D4—91no—
904C4×D4—91no—
905C4×D4—92no—
906C4×D4—92no—
907#117—31no—
908#117—32no—
909#117—32no—
910#117—92no—
911#117—91no—
912#117—91no—
913#117—92no—
914#117—92no—
915#117—92no—
916#117—92no—
917#117D3211yescharacteristic
918C2×C4⋊C4—31no—
919C2×C4⋊C4—92no—
920C2×C42—91no—
921C2×C42—92no—
922C23×C3—21no—
923C23×C3—31no—
924C23×C3—32no—
925C23×C3—31no—
926C23×C3C23×D311yescharacteristic
927C23×C3C23×D311yescharacteristic
928C22×D3—32no—
929C22×D3—32no—
930C22×D3—62no—
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D312yes—
933C22×D3C23×D311yescharacteristic
934C3×Q8—62no—
935C3×Q8—122no—
936C3×D4—62no—
937C3×D4—122no—
938C3×D4—121no—
939C3×D4—121no—
940C3×D4—122no—
941C2×C3×C4—24no—
942C2×C3×C4—22no—
943C2×C3×C4—22no—
944C2×C3×C4—21no—
945C2×C3×C4—21no—
946C2×C3×C4—22no—
947C2×C3×C4—22no—
948C2×C3×C4—32no—
949C2×C3×C4—31no—
950C2×C3×C4—31no—
951C2×C3×C4—32no—
952C2×C3×C4—32no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—31no—
956C2×C3×C4—31no—
957C2×C3×C4—62no—
958C2×C3×C4—62no—
959C2×C3×C4—122no—
960C2×C3×C4—122no—
961C2×C3×C4C23×D311yescharacteristic
962C2×C3×C4C23×D311yescharacteristic
963C2×C3×C4C23×D312yes—
964C2×C3×C4C23×D312yes—
965C2×C3×C4C23×D312yes—
966C2×C3×C4C23×D312yes—
967C2×C3×C4C23×D311yescharacteristic
968C2×C3×C4C23×D311yescharacteristic
969#67—41no—
970#67—41no—
971#67—42no—
972#67—64no—
973#67—64no—
974#67—64no—
975#67—64no—
976#67—68no—
977#67—122no—
978#67—122no—
979#67—122no—
980#67—122no—
981#67—121no—
982#67—121no—
983C2×Dic3—32no—
984C2×Dic3—32no—
985C2×Dic3—31no—
986C2×Dic3—31no—
987C2×Dic3—31no—
988C2×Dic3—31no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—61no—
994C2×Dic3—61no—
995C2×Dic3—62no—
996C2×Dic3—61no—
997C2×Dic3—61no—
998C2×Dic3—64no—
999C2×Dic3—64no—
1000C2×Dic3—122no—
1001C2×Dic3—121no—
1002C2×Dic3—121no—
1003C2×Dic3—121no—
1004C2×Dic3—121no—
1005C2×Dic3—122no—
1006C2×Dic3—122no—
1007C2×Dic3C23×D312yes—
1008C2×Dic3C23×D311yescharacteristic
1009C2×Dic3C23×D311yescharacteristic
1010C2×Dic3C23×D312yes—
1011C2×Dic3C23×D312yes—
1012C2×Dic3C23×D311yescharacteristic
1013C2×Dic3C23×D311yescharacteristic
1014C2×Dic3C23×D311yescharacteristic
1015C2×Dic3C23×D311yescharacteristic
1016D12—22no—
1017D12—42no—
1018D12—64no—
1019D12—62no—
1020D12—62no—
1021D12—122no—
1022D12—122no—
1023D12—122no—
1024D12—122no—
1025C4×D3—22no—
1026C4×D3—22no—
1027C4×D3—42no—
1028C4×D3—42no—
1029C4×D3—64no—
1030C4×D3—64no—
1031C4×D3—64no—
1032C4×D3—64no—
1033C4×D3—68no—
1034C4×D3—122no—
1035C4×D3—122no—
1036C4×D3—122no—
1037C4×D3—122no—
1038C4×D3—124no—
1039C4×D3—124no—
1040C4×D3—122no—
1041Dic6—22no—
1042Dic6—34no—
1043Dic6—34no—
1044Dic6—42no—
1045Dic6—64no—
1046Dic6—64no—
1047Dic6—64no—
1048Dic6—121no—
1049Dic6—121no—
1050C2×C32—41no—
1051C2×C32C22×#4111yescharacteristic
1052C2×C32#58511yescharacteristic
1053C2×C32#58511yescharacteristic
1054C3⋊D3—42no—
1055C3×D3—41no—
1056C3×D3—41no—
1057C3×D3—42no—
1058#41—184no—
1059#41—184no—
1060C2×Q8—31no—
1061C2×Q8—32no—
1062C2×Q8—92no—
1063C2×Q8—91no—
1064C2×Q8—91no—
1065C2×Q8—184no—
1066C2×D4—31no—
1067C2×D4—31no—
1068C2×D4—32no—
1069C2×D4—31no—
1070C2×D4—32no—
1071C2×D4—92no—
1072C2×D4—92no—
1073C2×D4—92no—
1074C2×D4—92no—
1075C2×D4—92no—
1076C2×D4—92no—
1077C2×D4—91no—
1078C2×D4—91no—
1079C22×C4—31no—
1080C22×C4—31no—
1081C22×C4—32no—
1082C22×C4—32no—
1083C22×C4—92no—
1084C22×C4—92no—
1085C22×C4—92no—
1086C22×C4—91no—
1087C22×C4—91no—
1088C22×C4—92no—
1089C22×C4—92no—
1090C22×C4—92no—
1091C22×C4C2×D3211yescharacteristic
1092C4⋊C4—32no—
1093C4⋊C4—31no—
1094C4⋊C4—31no—
1095C4⋊C4—32no—
1096C4⋊C4—31no—
1097C4⋊C4—32no—
1098C4⋊C4—32no—
1099C4⋊C4—32no—
1100C4⋊C4—31no—
1101C4⋊C4—32no—
1102C4⋊C4—32no—
1103C4⋊C4—91no—
1104C4⋊C4—92no—
1105C4⋊C4—91no—
1106C4⋊C4—92no—
1107C4⋊C4—91no—
1108C4⋊C4—92no—
1109C4⋊C4—91no—
1110C4⋊C4—92no—
1111C4⋊C4—91no—
1112C4⋊C4—92no—
1113C4⋊C4—91no—
1114C4⋊C4—91no—
1115C4⋊C4—91no—
1116C4⋊C4—92no—
1117C4⋊C4—92no—
1118C4⋊C4C2×D3211yescharacteristic
1119C4⋊C4C2×D3211yescharacteristic
1120C22⋊C4—31no—
1121C22⋊C4—31no—
1122C22⋊C4—32no—
1123C22⋊C4—31no—
1124C22⋊C4—32no—
1125C22⋊C4—32no—
1126C22⋊C4—32no—
1127C22⋊C4—32no—
1128C22⋊C4—32no—
1129C22⋊C4—31no—
1130C22⋊C4—92no—
1131C22⋊C4—92no—
1132C22⋊C4—92no—
1133C22⋊C4—92no—
1134C22⋊C4—91no—
1135C22⋊C4—91no—
1136C22⋊C4—91no—
1137C22⋊C4—92no—
1138C22⋊C4—91no—
1139C22⋊C4—92no—
1140C22⋊C4—91no—
1141C22⋊C4—91no—
1142C22⋊C4—92no—
1143C22⋊C4—92no—
1144C22⋊C4—92no—
1145C22⋊C4C2×D3212yes—
1146C42—32no—
1147C42—32no—
1148C42—31no—
1149C42—31no—
1150C42—92no—
1151C42—92no—
1152C42—92no—
1153C42—91no—
1154C42—91no—
1155C42—92no—
1156C42—91no—
1157C42—92no—
1158C42—91no—
1159C42C2×D3212yes—
1160C22×C3—22no—
1161C22×C3—21no—
1162C22×C3—21no—
1163C22×C3—21no—
1164C22×C3—21no—
1165C22×C3—21no—
1166C22×C3—21no—
1167C22×C3—21no—
1168C22×C3—41no—
1169C22×C3—41no—
1170C22×C3—61no—
1171C22×C3—62no—
1172C22×C3—61no—
1173C22×C3—62no—
1174C22×C3—61no—
1175C22×C3—61no—
1176C22×C3—61no—
1177C22×C3—62no—
1178C22×C3—61no—
1179C22×C3C24×D311yescharacteristic
1180C22×C3C24×D311yescharacteristic
1181C2×D3—21no—
1182C2×D3—21no—
1183C2×D3—22no—
1184C2×D3—21no—
1185C2×D3—22no—
1186C2×D3—21no—
1187C2×D3—21no—
1188C2×D3—22no—
1189C2×D3—21no—
1190C2×D3—64no—
1191C2×D3—62no—
1192C2×D3—62no—
1193C2×D3—62no—
1194C2×D3—62no—
1195C2×D3—62no—
1196C2×D3—62no—
1197C2×D3—122no—
1198C2×D3—122no—
1199C3×C4—22no—
1200C3×C4—21no—
1201C3×C4—21no—
1202C3×C4—22no—
1203C3×C4—22no—
1204C3×C4—22no—
1205C3×C4—22no—
1206C3×C4—22no—
1207C3×C4—42no—
1208C3×C4—42no—
1209C3×C4—61no—
1210C3×C4—62no—
1211C3×C4—61no—
1212C3×C4—62no—
1213C3×C4—61no—
1214C3×C4—61no—
1215C3×C4—61no—
1216C3×C4—61no—
1217C3×C4—62no—
1218C3×C4D3×#4112yes—
1219C3×C4D3×#4112yes—
1220Dic3—22no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—21no—
1224Dic3—22no—
1225Dic3—21no—
1226Dic3—21no—
1227Dic3—22no—
1228Dic3—21no—
1229Dic3—34no—
1230Dic3—34no—
1231Dic3—64no—
1232Dic3—62no—
1233Dic3—62no—
1234Dic3—61no—
1235Dic3—61no—
1236Dic3—61no—
1237Dic3—61no—
1238Dic3—61no—
1239Dic3—61no—
1240Dic3—61no—
1241Dic3—61no—
1242Dic3—121no—
1243Dic3—121no—
1244C32#352411yescharacteristic, complemented, Sylow
1245C23—31no—
1246C23—31no—
1247C23—32no—
1248C23—92no—
1249C23C22×D3211yescharacteristic
1250Q8—62no—
1251Q8—94no—
1252Q8—122no—
1253Q8—184no—
1254Q8—361no—
1255D4—62no—
1256D4—122no—
1257D4—121no—
1258D4—121no—
1259D4—122no—
1260D4—184no—
1261D4—184no—
1262D4—182no—
1263D4—362no—
1264D4—362no—
1265D4—362no—
1266D4—362no—
1267D4—361no—
1268C2×C4—22no—
1269C2×C4—31no—
1270C2×C4—31no—
1271C2×C4—31no—
1272C2×C4—32no—
1273C2×C4—31no—
1274C2×C4—32no—
1275C2×C4—31no—
1276C2×C4—32no—
1277C2×C4—31no—
1278C2×C4—62no—
1279C2×C4—62no—
1280C2×C4—92no—
1281C2×C4—91no—
1282C2×C4—91no—
1283C2×C4—91no—
1284C2×C4—91no—
1285C2×C4—122no—
1286C2×C4—122no—
1287C2×C4—184no—
1288C2×C4—184no—
1289C2×C4—184no—
1290C2×C4—362no—
1291C2×C4—362no—
1292C2×C4—362no—
1293C2×C4—361no—
1294C2×C4—361no—
1295C2×C4C22×D3212yes—
1296C2×C4C22×D3211yescharacteristic
1297C2×C4C22×D3212yes—
1298C2×C4C22×D3211yescharacteristic
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—21no—
1302C2×C3—42no—
1303C2×C3—41no—
1304C2×C3—41no—
1305C2×C3—121no—
1306C2×C3—122no—
1307C2×C3—121no—
1308C2×C3C2×D3×#4111yescharacteristic
1309C2×C3C2×D3×#4111yescharacteristic
1310C2×C3#596411yescharacteristic
1311C2×C3#596411yescharacteristic
1312C2×C3#596611yescharacteristic
1313C2×C3#596811yescharacteristic
1314D3—41no—
1315D3—41no—
1316D3—42no—
1317D3—124no—
1318D3—122no—
1319D3—122no—
1320C22—21no—
1321C22—21no—
1322C22—21no—
1323C22—61no—
1324C22—61no—
1325C22—62no—
1326C22—61no—
1327C22—62no—
1328C22—61no—
1329C22—61no—
1330C22—62no—
1331C22—61no—
1332C22—182no—
1333C22—182no—
1334C22—182no—
1335C22C23×D3211yescharacteristic
1336C4—21no—
1337C4—22no—
1338C4—22no—
1339C4—61no—
1340C4—61no—
1341C4—62no—
1342C4—61no—
1343C4—62no—
1344C4—61no—
1345C4—62no—
1346C4—61no—
1347C4—61no—
1348C4—94no—
1349C4—181no—
1350C4—181no—
1351C4—181no—
1352C4—181no—
1353C4#6430612yes—
1354C3—21no—
1355C3#8684311yescharacteristic, complemented
1356C3#8696511yescharacteristic, complemented
1357C2—41no—
1358C2—121no—
1359C2—121no—
1360C2—122no—
1361C2—362no—
1362C2C2×#6430611yescharacteristic
1363C2#1059669511yescharacteristic
1364C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10595993C2semidirect
2. C3×#5532C2semidirect
3. C3×#5529C2semidirect
4. #10595033C2semidirect
5. #10594965C2semidirect
6. #10594919C2semidirect
7. #10594916C2semidirect
8. #10594566C2semidirect
9. #10594559C2semidirect
10. #10594525C2semidirect
11. #10594501C2semidirect
12. #10594359C2semidirect
13. #10594357C2semidirect
14. #10594343C2semidirect
15. #10594318C2semidirect
16. #10594219C2semidirect
17. #10594152C2semidirect
18. #10594151C2semidirect
19. #10594124C2semidirect
20. #10593980C2semidirect
21. #10593943C2semidirect
22. #10593930C2semidirect
23. #10593918C2semidirect
160. #5532D3semidirect
163. #5529D3semidirect
1244. C32#3524semidirect
1355. C3#86843semidirect
1356. C3#86965semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105959932
C3×#55322
C3×#55292
#105950332
#105949652
#105949192
#105949162
#105945662
#105945592
#105945252
#105945012
#105943592
#105943572
#105943432
#105943182
#105942192
#105941522
#105941512
#105941242
#105939802
#105939432
#105939302
#105939182
#869653
#868433